document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388932>Question 388932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> prove that if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275438 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=275438\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the diagonals of a parallelogram are perpendicular, then there would be four right triangles that are congruent (by the LL theorem)and side by side each other. ( This is due to the fact that the diagonals of a parallelogram bisect each other.)  The hypotenuses of these congruent right triangles are the sides of this parallelogram, and since they (the hypotenuses) are congruent, the parallelogram is a rhombus. </SPAN>\n" );
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